Domain-Functions
state the domain and range of the function

According to the given logarithm 3 log₄ x+2 log₄x written as a single logarithm 5 log₄(x).

When they urge you to "simplify" a log expression, it usually implies they've given you a bunch of log terms, each with a simple argument, and they'd like you to combine them all into one log with a sophisticated argument. In this sense, "simplifying" usually means the inverse of "growing."

3 log₄ x+2 log₄ x

Add similar elements:

So:

This expression can be written as:

3 log₄ (x)+2 log₄ (x) = 5 log₄(x)

According to the given logarithm 3 log₄ x+2 log₄x written as a single logarithm 5 log₄(x).

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Considering the definition of an inequality, all possible values for the length of the sides of the square picture are greater than 3 inches but less than 8.75 inches.

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

An inequality contains one or more unknown values ​​called unknowns, in addition to certain known data.

Solving an inequality consists of finding all the values ​​of the unknown for which the inequality relation holds.

The perimeter of a two-dimensional figure is the distance around the figure. That is, the perimeter of a flat geometric figure is called the length of its contour.

The perimeter is the measurement obtained as a result of the sum of the sides of a flat geometric figure.

A square is a flat geometric figure that has four equal sides, so the expression to calculate the perimeter of a square is:

Perimeter= 4× length of the sides

In this case, you know that the perimeter of a square picture frame is to be at most 35 inches but no less than 12 inches.

Being "S" the length of the sides of the square picture, the inequality that expresses the previous relationship is

12 inches< 4×S ≤35 inches

Solving:

12 inches ÷4< S ≤35 inches ÷4

3 inches <S≤ 8.75 inches

Finally, all possible values for the length of the sides of the square picture are greater than 3 inches but less than 8.75 inches.

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The value of x for the equation log₄64=x is 3.

Due of their connection to exponential functions, logarithmic functions are crucial. Exponential equations and the characteristics of exponential functions may both be investigated using logarithms. Additionally, they will be of great service in calculus, where they will be used to determine the slope of specific functions and the region enclosed by particular curves. They also have useful uses in economics.

Given,

log₄64=x

It can be expressed as -

64 = 4ˣ

4³ = 4ˣ

As base is same,

x = 3

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After multiplying, the answer of (4+2√3)(6-3√3) is 15.

1. Divide the radicands by two. Under the radical sign, there is a number called a radicand. 2. Multiple the integers as though they were whole numbers in order to multiply radicands. Keep the product under a single radical sign at all times.

3. Remove any perfect squares from the radicand by factoring. Check to determine whether the radicand is a factor of any perfect squares to do this.

4. Before the radical sign, place the square root of the ideal square. Keep the second element in the radical sign.

5. Square the root of a square. A square root may occasionally need to be multiplied by itself.

(4+2√3)(6-3√3)

⇒ 4 ×6 + 4 × -3√3 + 2√3 × 6 - 2√3 × 3√3

⇒ 24 - 12√3 + 12√3 - 9

⇒ 15

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By basic algebra, we can say that: the satellite to run for about 130 days if it requires 15W of power.

Given:

To find: t when P = 15.

Finding:

On substituting the given values in the given formula, by basic algebra, we get:

15 = 50 [tex]e^{\frac{-t}{250}}[/tex]

=> [tex]\frac{15}{50}=\frac{3}{10}[/tex] = [tex]e^{\frac{-t}{250}}[/tex]

=> log [tex]\frac{3}{10}[/tex] = [tex]\frac{-t}{250}[/tex]

=> - 0.522 = [tex]\frac{-t}{250}[/tex]

=> 130.5 = t

Hence, the satellite to run for about 130 days if it requires 15W of power, as solved by basic algebra.

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The equation of the line in fully simplified slope-intercept form is y = -x + 3

From the question, we are to write the equation of the line in fully simplified slope-intercept form

The slope-intercept form of the equation of a straight line is given as

y = mx + b

Where m is the slope of the line

and b is the y-intercept

From the graph,

The y-intercept is 3

∴ b = 3

Now, we will determine the slope, m, of the line

Given any two points (x₁, y₁) and (x₂, y₂) on a line, the slope, m, of the line is

m = (y₂ - y₁)/(x₂ - x₁)

Picking the points, (0, 3) and (2, 1)

m = (1 - 3)/(2 - 0)

m = -2/2

m = -1

Putting in the slope, m, and the y-intercept, b into the equation of a line

y = mx + b

We get

y = -1(x) + 3

Simplify

y = -x + 3

Hence, the equation of the line in fully simplified slope-intercept form is y = -x + 3

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The linear function slope, f(2)=-4, and f(3)=2 the equation for f(x) is y = 6x +6

This is the same as finding the line that goes through the two points (3,2) and (2,-4)

It has slope[tex]\frac{-6}{-1}[/tex] = 6 = [tex]\frac{(-4-2)}{(2-3)}[/tex] = m=6.  slope = rise/run.  or change in y coordinates/change in x coordinates

The y-intercept is given by(2,-4) as 6, b= 6. so plug that into the slope-intercept equation

y= MX + b

y = 6x +6

It's just a coincidence they both happened to = 6. m=b=6

In Mathematics, a slope of a line is the change in y coordinate with respect to the change in x coordinate.  the web change in the y-coordinate is represented by Δy and the net change in the x-coordinate is represented by Δx. Where “m”  is the slope of a line. So, tan θ to be the slope of a line.

Pick two points on the road and determine their coordinates. Determine the difference in y-coordinates of those two points (rise). Determine the difference in x-coordinates for these two points (run). Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).

Whenever the equation of a line is written within the form y = MX + b,  it's called the slope-intercept form of the equation. The m  is the slope of the line. And b  is that the b in the point that is the y-intercept (0, b).  for instance, for the equation y = 3x – 7, the slope is 3,  and therefore the y-intercept is (0, −7).

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Answer:

12-6 is the right answer

Step-by-step explanation:

Multiple 3 to 4 which is 12 and then then multiple it with two which is 6 so the answer is 12-6

Greetings from Brasil...

According to trigonometry, we have:

COS α = SIN (90 - α)

SIN α = COS(90 - α)

Then

(SIN 45).(COS 45) + [(SIN 30).(COS 60)] - COS² 30]

(√2/2).(√2/2) + [(1/2).(1/2)] - (√3/2)² = 0

The square tiles needed to cover the floor will be 9.

From the information, the square floor has a side length of (9/2) units and the square tile has a side length of (3/2)² units.

Therefore, the square tiles needed to cover the floor will be:

= Area of floor / Area of one tile

= (9/2)² / (3/2)²

= (9 × 9)/(3 × 3)

= 81 / 9.

= 9

Therefore, the square tiles needed to cover the floor will be 9.

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√19 + √3 is greater than √5 +√13.

We first relate the two numbers √19 + √3 and √5 +√13 through an inequality and check if it is true.

First suppose that √19 + √3 > √5 +√13

On squaring both sides and using the identity [tex](a+b)^2=a^2+b^2+2ab[/tex],

⇒ [tex](\sqrt{19}+\sqrt{3})^2 > (\sqrt{5}+\sqrt{13})^2\\22+2\sqrt{57} > 18+2\sqrt{65} \\[/tex]

Dividing by 2 on both sides,

⇒ [tex]11+\sqrt{57} > 9+\sqrt{65}[/tex]

Subtracting 9 from both sides,

⇒ [tex]2+\sqrt{57} > \sqrt{65}[/tex]

Squaring again, we get,

⇒ [tex]61 +4\sqrt{57} > 65[/tex]

Subtract 61 on both sides,

⇒ [tex]4\sqrt{57} > 4[/tex]

Dividing by 4 on both sides,

⇒ [tex]\sqrt{57} > 1[/tex]

Finally squaring once more,

⇒ 57 > 1, which is true.

So our assumption that √19 + √3 > √5 +√13 is right.

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The growth factor for the annual rate of change +100% is 2.

A quantity must vary by a specific percentage each time period in order for growth or decay to be exponential.

With the function displayed to the right, you may represent exponential growth or decay.

A(x) = a( 1 + r)ˣ

Where A is the amount after x time periods, a is the initial amount, x is the number of time periods, and r is the rate of change.

Now, we have the annual rate of change as:

r = + 100% = + 1

From the function A(x) = a( 1 + r)ˣ , the corresponding factor is 1 + r.

So, let B = 1 + r

B = 1 + r

B = 1 + (+1)

B = 2

Now, the value of B is greater than 1 therefore, the corresponding growth factor is 2.

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The rate of lemon used in lemons per cup of lemonade is 120%

Based on the given conditions,

18/15 = 6/5

Cross out the common factor: 6/5 x 20/20

Multiply a number to both the numerator and the denominator,

6 x 20/ 5 x 20.

Write as a single fraction, 120/100

Rewrite a fraction with denominator equals 100 to a percentage which is 120%.

part of a whole expressed in hundredths a high percentage of students attended. b : the result obtained by multiplying a number by a percent the percentage equals the rate times the base. 2a : a share of winnings or profits.​5 percent​ is ​one half of 10 percent​. To calculate 5 percent of a number, simply divide 10 percent of the number by 2. For example, 5 percent of 230 is 23 divided by 2, or 11.5.

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The inverse for the function f (x) = 1.2 x⁴ will be f ⁻¹ (x) = ⁴√ ( 5 x / 6).

We are given the function:

f (x) = 1.2 x⁴

we need to find the inverse of the function.

First we will write the function in the form of x.

y = 1.2 x⁴

y / 1.2 =  x⁴

x = ⁴√ ( y / 1.2)

x = ⁴√ ( 5 y / 6)

So, the inverse function will be:

f ⁻¹ (x) = ⁴√ ( 5 x / 6)

Therefore, the inverse for the function f (x) = 1.2 x⁴ will be f ⁻¹ (x) = ⁴√ ( 5 x / 6).

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Answer:

if i am looking at this correct then number 4 is 6 faces number 5 is 5 and number 6 is 5

Answer:

y = 12x

Step-by-step explanation:

For an equation to be parallel the slopes must be the same.  The slope from the equation is 12.

y = mx + b  is the slope-intercept form of a line'

y = 12x + 3.  The m is the slope and that is 12 ion this equation.

We will use the slope (12), the x (0) and the y (0) to write the new equation.  We need to find the y intercept.  We can see from the ordered pair given that the y - intercept would be zero, but here is another way to check.

y = mx + b

0 = 12(0) + b

0 = 0 + b

0 = b

y = 12x + 0

or

y = 12x

the slope of that equation is -3/5

If you climb up 5 flights of stairs it will give zero according to the given condition. The correct option is C.

What about expression?

Expression in maths is defined as the combination of numbers, variables, and functions by using operators like addition, subtraction, multiplication, and division.

Given some situations which of those can be represented with an integer​ that, when combined with the opposite of −5​, makes​ 0?

If you climb up 5 flights of stairs means you move forward upwards then it will give the positive value of 5.

Now, when it is added to -5 then it will give zero.

= 5+(-5)

= 5-5

= 0

Therefore, If you climb up 5 flights of stairs it will give zero by combining the opposite of that according to the given question. The correct option is C.

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The question is incomplete.

Kindly, find the complete question below.

Which of these situations can be represented with an integer​ that, when combined with the opposite of −5​, makes​ 0?

Select all that apply.

A. You earn ​$5 from your chores.

B. You walk down 5 flights of stairs.

C. You climb up 5 flights of stairs.

D. The temperature drops 5°F.

E. You spend ​$5 on a game.

Answer:

The missing value of the table is 1,800 .

The number of books that Mrs. Johnson bought is 8 books.

How many magazines did she buy:

Let x represent the number of books she bought

The first step is to formulate an equation

12x + 16 = 112 dollars

The second step is to transpose

12x=112-16  

12x = 96

The third step is to divide both sides by 12

x=96/12  

x = 8

In conclusion, the number of books that Mrs. Johnson bought is eight books.

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Answer:

53°

Step-by-step explanation:

Corresponding angles are congruent

Answer:

-3

Step-by-step explanation:

p(0) = (0^2) + 5(0) - 3

p(0) = 0 + 0 - 3

p(0) = -3

the linear equation such that it is parallel to the line:

y = -2x + 5

And that it passes through the point (-2, -4) is y = -2*x - 8

Here we want to find a linear equation such that it is parallel to the line:

y = -2x + 5

And that it passes through the point (-2, -4)

Remember that two lines are parallel if and only if the lines have the same slope and different y-intercept.

Then our line is something like:

y = -2*x + b

To find the value of b, we replace the values of the given point:

-4 = -2*-2 + b

-4 = 4 + b

-4 - 4 = b = -8

We conclude that the linear equation is y = -2*x - 8

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By  -236 dB approximately the noise is reduced on imparting sound barrier.

Given that, the foreman of a construction team puts up a sound barrier that reduces the intensity of the noise by 50%. Let the intensity of the sound is I and it is reduced 50% then, new intensity of sound will be

new intensity after reduction = I-50% of I = I/2

Now, the Loudness is calculated by using the formula,

L = 10 log I/I₀

now, I = I/2 and I₀ = 10⁻¹² W/m²

So, we have to find out by how many decibels(dB) the noise is reduced after putting a sound barrier.

This will simply be calculated by subtracting the two noise before and after the sound barrier indulgence. Let's proceed to solve accordingly.

L = 10 log I/I₀ - 10 log I/2I₀

= 10(log I/I₀ - log I/2I₀)

By using the logarithmic property, log(a/b) = log a - log b

= 10(log I-log I₀-log I-log2I₀)

= 10(-log I₀ - log2I₀)

= -10(log I₀ + log2I₀)

Now, we know that, I₀ = 10⁻¹² W/m²

Put the value of I₀ and solve accordingly, we get

L = -236 dB approximately

Therefore, L = -236 dB approximately is the required answer.

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The probability is 0.357

Given that,

The system has at least one type of defect,

Suppose, A certain system can experience three different types of defects.

Let  (i = 1,2,3) denote the event that the system has a defect of type i.

Suppose that the following probabilities are,

P(A1)=0.11

P(A2)=0.08

P(A3)=0.05

P(A1UA2)=0.13

P(A1UA3)=0.13

P(A2UA3)=0.11

P(A1nA2nA3)=0.01

P(A1nA2)=0.06

P(A1nA3)=0.03

P(A2nA3)=0.02

P(A1UA2UA3)=0.14

P= P(A1) + P(A2) + P(A3) - 2P(A1UA2) - 2P(A1UA3) - 2P(A2UA3) +       3P(A1nA2nA3) / P(A1UA2UA3)

P= 0.11 + 0.08 + 0.05 -2*0.06 -2*0.03 -2*0.02 +3*0.01 / 0.14

P=0.357

Hence, the probability is 0.357

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We need to calculate the probability that it has exactly one type of defect

Using given data

+ +

P =

Put the value into the formula

Hence, The probability is 0.357

The value of function  f(x) = x+4 when x=3 is 7.

By considering given function

f(x) = x+4

f(3)= 3+4

f(3)=7

A mathematical expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functions are fundamental for constructing physical relationships.

Four broad categories can be used to classify different types of functions. One to one function, many to one function, onto function, one to one and into function—all based on the element.

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The value of function f(x) = x+4 by evaluating it when x = 3 will be 7.

A function is defined as anything from a set X to a set Y assigns to each element of X exactly one element of Y.

We are given a function:

f(x) = x + 4

We need to evaluate for x = 3.

We will do this by putting x = 3 in the function given to us.

So, we get that:

f ( 3 ) = 3 + 4

Adding the terms, we get that:

f ( 3 ) = 7

Therefore, value of function f(x) = x+4 by evaluating it when x = 3 will be 7.

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The value of the function f(-8) is -512

A function is defined as an expression, rule or law that shows the relationship between two variables;

Given the function:

f(x)= x × x²

To determine the function f(-8), we substitute the value of x  as -8 in the function

With this, we have;

f(-8) = (-8) × (-8)²

expand the bracket

f(-8) = -8 × 64

Multiply through

f(-8) = - 512

The value of the function is -512

Thus, the value of the function f(-8) is -512

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